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Make 24

Date: 01/03/2003 at 06:01:51
From: Hasan
Subject: Make 24 using 1,3,4,6

We have to make 24 by using 1, 3, 4, and 6. We can use +,-,*,/. 
What is the answer? Is it (14-6) * 3 = 24?


Date: 01/03/2003 at 13:01:33
From: Doctor Ian
Subject: Re: Make 24 using 1,3,4,6

Hi Hasan,

That certainly looks like an answer, assuming you can place digits
together as you've done (i.e., making '14' from '1' and '4'). You'd
have to check with your teacher to see if it's considered 'legal'.  

Note that if you can use exponents, an answer would be

   3
  1  * 4 * 6

However, there's a sneaky way to get what amounts to a fifth number,
by doing this:

          a
  24 = -------
            c
        b - -
            d


           a
  24 = --------
        bd   c
        -- - -           Get a common denominator
         d   d


           a
  24 = --------
        bd - c
        ------           Subtract
           d


          ad
  24 = --------          Invert and multiply
        bd - c


Now, this is a little simpler, because we need to get a multiple of 24
on top, and something on the bottom that will reduce it back to 24. 

The obvious way to do that would be to get 24 on top, and 1 on the 
bottom:

         6*4
  24 = --------          Invert and multiply
        b*4 - c
        
Can you get the denominator to be equal to 1, using 1 and 3 as 
possible values for b and c? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
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